PDEtools[CharacteristicQ] - compute the characteristic of a point symmetry represented by its infinitesimals

Calling Sequence

CharacteristicQ(S, DepVars, 'options'='value')

Parameters

S

-

a list with the infinitesimals of a symmetry generator or the corresponding infinitesimal generator operator

DepVars

-

a function or a list of them indicating the dependent variables of the problem

checktype = ...

-

optional - can be true (default) or false, to have or have not inserted a check-of-type for the arguments of the output procedure

expanded = ...

-

optional - can be true or false (default), to have or have not expanded the sums entering the body of the output procedure

jetnotation = ...

-

(optional) can be true (default, the notation found in S), false, jetvariables, jetvariableswithbrackets, jetnumbers or jetODE; to respectively return or not using the different jet notations available

Description

•

The CharacteristicQ command computes the characteristic of a point symmetry represented by its infinitesimals or the corresponding infinitesimal generator operator. That is, for a PDE problem with n independent and m dependent variables, given a related list of infinitesimals ξ1&comma;`...`&comma;ξn&comma;η1&comma;`...`&comma;ηm, CharacteristicQ computes the procedure

The sum in the body of this operator returned by CharacteristicQ is not expanded unless explicitly requested using the optional argument expanded. Also, jetnotation is used in this operator and a check-of-type for the value of m is automatically inserted unless explicitly requested otherwise with the optional arguments jetnotation = false and/or checktype = false - see the examples below.

•

To avoid having to remember the optional keywords, if you misspell a keyword, or a portion of it, a matching against the correct keywords is performed, and when there is only one match, the input is automatically corrected.